400px, A dispersion fan diagram (left) in comparison with a box plot
A fan chart is made of a group of dispersion fan diagrams,
which may be positioned according to two categorising dimensions.
A ''dispersion fan diagram'' is a circular diagram which
reports the same information about a dispersion as a
box plot:
namely
median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic fe ...
,
quartile
In statistics, a quartile is a type of quantile which divides the number of data points into four parts, or ''quarters'', of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a ...
s, and two extreme values.
Elements
The elements of a dispersion fan diagram
are:
# a ''circular line'' as scale
# a ''diameter'' which indicates the median
# a ''fan'' (a segment of a circle) which indicates the quartiles
# two ''feathers'' which indicate the extreme values.
The scale on the circular line begins at the left
with the starting value (e. g. with zero).
The following values are applicated clockwise.
The white tail of diameter indicates the median.
The dark fan indicates the dispersion of the middle half of the observed
values; thus it encompasses the values from the first to the third quartile.
The white feathers indicate the dispersion of the middle 90% of the
observed values.
The length of the white part of the diameter corresponds with the number
of observations.
Application
A fan chart gives a quick summary of observed values which depend from two variables. This is possible thanks of a dense representation
and a constant size which does not depend on the size of the single dispersion fan diagrams.
An essential advantage compared to a sequence of box plots
is the possibility to compare dispersion fan diagrams not only within one direction
but within two directions (horizontally and vertically).
Example
The following example presents data from the data set ''MathAchieve''
which is part of the
R packag
''nlme''of José Pinheiro et al.
It contains mathematics achievement scores of 7185 students.
The students are categorised
according to sex and membership of a minority ethnic group.
The graphics show the mathematics achievement scores in dependency
on the socio-economic status of the students (x axis)
and on the average socio-economic status of all students
at the same school (y axis).
The four graphic panels differentiate the students
according to sex and membership of a minority ethnic group.
The fan charts reveals clearly how the median value
is partially following a big main tendency
while the values of the single subgroups (with the cells) scatter largely
what could lead to doubts about a possible correlation.
See also
*
Box plot
References
External links
* Fischer, Wolfram (2012)
''Streuungsfächerkarten und pseudogeografische Anordnungen.'' Mit Beispielen zum verfügbaren Einkommen und zu Krankenkassenprämien in der Schweiz Swiss Days of Official Statistics, Vaduz LI, 2012.
* Fischer, Wolfram (2010)
''Visualising Twofold Dependencies by Fan Charts'' ZIM.
{{Statistics, descriptive
Statistical charts and diagrams